AC Bridge: Construction, Working Principle, Types, and Balance Conditions

Introduction

AC bridges are electrical circuits used for the measurement of inductance, capacitance, resistance, dissipation factor, storage factor, and other AC parameters. These bridges operate only on alternating current and are commonly used for precise measurement applications.

An AC bridge also provides a phase-shifting network and a feedback path to oscillators, making it a key component in AC measurement systems.

AC Bridge Network Construction

An AC bridge consists of four arms (each containing an impedance), four junction nodes, an AC source, and a detector. The source and detector are always connected to opposite nodes. If the source and detector are connected to the same nodes, the detector senses the full source voltage, and the bridge can never reach balance.

Balance Conditions

A bridge is considered balanced when:

• The current through the detector is zero
• The potential difference across the detector is zero

This condition is known as the null condition. At balance, even though AC is supplied, no voltage appears across the detector, similar to a Wheatstone bridge in DC circuits.

How Does a Bridge Circuit Work?

An AC bridge operates using two voltage dividers connected across the same AC source. A null detector (headphones, vibration galvanometer, or tuned amplifier) is connected between the two dividers.

When the bridge is balanced:

Z₁ × Z₄ = Z₂ × Z₃

Any one of the four impedances can be unknown. When balance is achieved, the unknown value can be calculated using the known three impedances.

One major advantage of using an AC bridge (or DC Wheatstone bridge) is that the supply voltage does not affect measurement accuracy. A higher supply voltage improves sensitivity but does not change the value calculated.

Types of AC Bridges

• Capacitance Comparison Bridge
• Inductance Comparison Bridge
• Maxwell’s Bridge
• Hay’s Bridge
• Anderson Bridge
• Schering Bridge
• Wien Bridge

Conditions for Balancing an AC Bridge

To measure an unknown resistance, inductance, or capacitance using an AC bridge, the bridge must first be balanced.

At balance:

V₁ = V₂   and   V₃ = V₄

If the AC source voltage is V and the potential drops across impedances Z1, Z2, Z3, Z4 are V1, V2, V3, V4, then at balance the impedance relationship must satisfy:

Z₁ × Z₄ = Z₂ × Z₃

Admittance Form

Since Z = 1/Y, the balance equation can also be expressed using admittances as:

Y₁ × Y₄ = Y₂ × Y₃

Polar Form

In polar notation, the magnitude and phase relationships must satisfy:

• |Z₁| × |Z₄| = |Z₂| × |Z₃|
• θ₁ + θ₄ = θ₂ + θ₃

Thus, both magnitude and phase conditions must be simultaneously satisfied for the AC bridge to achieve exact balance.